{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empirical Approximation overview\n",
    "\n",
    "For most models we use sampling MCMC algorithms like Metropolis or NUTS. In PyMC3 we got used to store traces of MCMC samples and then do analysis using them. There is a similar concept for the variational inference submodule in PyMC3: *Empirical*. This type of approximation stores particles for the SVGD sampler. There is no difference between independent SVGD particles and MCMC samples. *Empirical* acts as a bridge between MCMC sampling output and full-fledged VI utils like `apply_replacements` or `sample_node`. For the interface description, see [variational_api_quickstart](variational_api_quickstart.ipynb). Here we will just focus on `Emprical` and give an overview of specific things for the *Empirical* approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import theano\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "np.random.seed(42)\n",
    "pm.set_tt_rng(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multimodal density\n",
    "Let's recall the problem from [variational_api_quickstart](variational_api_quickstart.ipynb) where we first got a NUTS trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '18726' (I am process '18876')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /Users/twiecki/.theano/compiledir_Darwin-18.2.0-x86_64-i386-64bit-i386-3.6.7-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '18726' (I am process '18876')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /Users/twiecki/.theano/compiledir_Darwin-18.2.0-x86_64-i386-64bit-i386-3.6.7-64/lock_dir\n",
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '18726' (I am process '18876')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /Users/twiecki/.theano/compiledir_Darwin-18.2.0-x86_64-i386-64bit-i386-3.6.7-64/lock_dir\n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [x]\n",
      "Sampling 2 chains: 100%|██████████| 101000/101000 [00:51<00:00, 1963.57draws/s]\n",
      "/Users/twiecki/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "w = pm.floatX([.2, .8])\n",
    "mu = pm.floatX([-.3, .5])\n",
    "sd = pm.floatX([.1, .1])\n",
    "\n",
    "with pm.Model() as model:\n",
    "    x = pm.NormalMixture('x', w=w, mu=mu, sigma=sd, dtype=theano.config.floatX)\n",
    "    trace = pm.sample(50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great. First having a trace we can create `Empirical` approx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "**Single Group Full Rank Approximation**\n",
      "\n",
      "    Builds Approximation instance from a given trace,\n",
      "    it has the same interface as variational approximation\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(pm.Empirical.__doc__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "with model:\n",
    "    approx = pm.Empirical(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc3.variational.approximations.Empirical at 0x1c23a8abe0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This type of approximation has it's own underlying storage for samples that is `theano.shared` itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "histogram"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.44232642],\n",
       "       [0.43486722],\n",
       "       [0.57271322],\n",
       "       [0.58091718],\n",
       "       [0.38298766],\n",
       "       [0.38298766],\n",
       "       [0.33438251],\n",
       "       [0.7098557 ],\n",
       "       [0.61921361],\n",
       "       [0.54169809]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.histogram.get_value()[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100000, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.histogram.get_value().shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has exactly the same number of samples that you had in trace before. In our particular case it is 50k.  Another thing to notice is that if you have multitrace with **more than one chain** you'll get much **more samples** stored at once. We flatten all the trace for creating `Empirical`.\n",
    "\n",
    "This *histogram* is about *how* we store samples. The structure is pretty simple: `(n_samples, n_dim)` The order of these variables is stored internally in the class and in most cases will not be needed for end user"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc3.blocking.ArrayOrdering at 0x114162c88>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "approx.ordering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from posterior is done uniformly with replacements. Call `approx.sample(1000)` and you'll get again the trace but the order is not determined. There is no way now to reconstruct the underlying trace again with `approx.sample`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO (theano.gof.compilelock): Waiting for existing lock by process '18726' (I am process '18876')\n",
      "INFO (theano.gof.compilelock): To manually release the lock, delete /Users/twiecki/.theano/compiledir_Darwin-18.2.0-x86_64-i386-64bit-i386-3.6.7-64/lock_dir\n"
     ]
    }
   ],
   "source": [
    "new_trace = approx.sample(50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.69 s ± 68.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit new_trace = approx.sample(50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After sampling function is compiled sampling bacomes really fast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(new_trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You see there is no order any more but reconstructed density is the same.\n",
    "\n",
    "## 2d density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [x]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:04<00:00, 703.93draws/s]\n",
      "/Users/twiecki/anaconda3/lib/python3.6/site-packages/mkl_fft/_numpy_fft.py:1044: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  output = mkl_fft.rfftn_numpy(a, s, axes)\n"
     ]
    }
   ],
   "source": [
    "mu = pm.floatX([0., 0.])\n",
    "cov = pm.floatX([[1, .5], [.5, 1.]])\n",
    "with pm.Model() as model:\n",
    "    pm.MvNormal('x', mu=mu, cov=cov, shape=2)\n",
    "    trace = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "with model:\n",
    "    approx = pm.Empirical(trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(approx.sample(10000));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/twiecki/anaconda3/lib/python3.6/site-packages/seaborn/distributions.py:679: UserWarning: Passing a 2D dataset for a bivariate plot is deprecated in favor of kdeplot(x, y), and it will cause an error in future versions. Please update your code.\n",
      "  warnings.warn(warn_msg, UserWarning)\n",
      "/Users/twiecki/anaconda3/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c2174d400>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yFvPIFBUX4/qDF9h/2hUJyalYNGMClsyYWK2bmsmpaZg4dwlycnPx+PIZ1BdiO8BtO3bjvOtV+Hq8rtFNZ6Z2sDl25v9eYNBXrFi7AUHBIZg3ewaWLVlY7aARHhUDi2XWiPoWi7WW8zHHbGKFQZSI4PbeC47HL8D/axhaNlOCrdVcjB3aD7JCPNRDRIiITUBAaBS+RsQgOPIbouISkZKehfSsHFQ0SKonKor68rJQVW6Cls2aQLVZU3RorQ799lrV/lYgLiaGSaYDYTrAELYOR7D/lCs8fQPhZLMMio0aCNWGYqOGOGi/ESPMLLDv+BnYLF9c5THa7dqisLAQ4ZFRaM2Sg/3fY4Gd+eWICGfOX4T9LkcoKCjg+KF96GvUp9rteHr7Ye4ya4iKiODcIQd006t4+uZLcDg2Oh6Fl18gWig3wY61izF6UF/Uq1f5SDc5LQMvPHzwzjsA7z4HICmtZJ9SURERqLdQgoaKMvQ7tEGj+vJopCAPcfF64HA4EBURQWFRMbJz85Gdm4fUjCzEJCThvU8Qbjx9U9qGXnstDDXshvGDDSElKSH0tUtLSWLXOksY6LSHrcMRjJq7Ahf2b4Vqc+Ee3GrXuhUmjhyGc5dvwmLaJCg1Uay0fvs/94X9EhDIAvu/AJuKYX6prKxsrLXZhIdPnqGfkSF2bNuIhg2EG2n+0xO311iybjOUmzbBmf27oFJBQMvIyobDsfO4cOsRGijIYensKRg3rH+luVW+JSTjgbsHHr/2wqfAUBARGtWXRw8dbfTQaYfObTSh2VK5xg825eUXwOdrON5+/oJn7z8jKDwGDRXkMHPMYEwz7V/tUbz/1zCYL7WFlKQ4zu/bBrUWwgX3yJhv6DfaDMsXzMHCWWaV1uXxeNDtbogxI0dg4/o11eofU3vYHDvzfycqOgbT5/6B+IRErLBajDkzptVo7vnyrfuw3rYbHdu1wXEnuwrn0+89ew1bxyPIyMqB+ZihsJo9GfJysgLrpmdl48Grj7jz4h0++AYBANq3UsXAXvow6dkFbdVVflqulI/+X+F88Q7cPHwgJyONzUumY2S/ntVqIzAkAmZWGyAhLo5rR3YKvYpnyjwrxCcm4fmN81Ven9msecjKysLtqxer1Tem9ggb2EFEv/xHT0+PmP+WsPAI6mE8gPR6GtMnb58at3P83GVS1zOi6YtWUG5ensA66ZlZtMR2N6n3MqVRc5ZTQEiEwHp8Pp8++n0ly+0HqfXg6aRuYkYmM1fRPpcbFB2XWOM+1pR/SASNt9pM6iZmtNbhOOUXFFbr+ICQCOo4YCINnW5JuXn5Qh1z4dptUtczouCwiCrr7j14mDTb61J6eka1+sXUHgCeJESMZYGd+emiY76RQZ/+1LVPPwoKDqlxO3uPniZ1PSNasMqGCouKBNZx9/hM3UfOIC3D0bT/lCsVF3PL1SkoLKJL91/QUAtrUjcxo46mc2njgTP0JSSS+Hx+jftXG4q5XNp53JXUTcxoiMVaioxNqNbxbu+8SKP3SFptt0+o+rHxiaSuZ0RHzlyssq7np8+koa1D9x8+rlafmNojbGBnUzHMT8Xn82E2ax6+BAbh2oUzNc6dfuD4WTgcPomxwwfBbv3Kcqtn+Hw+Dpy5jL0nL0FTtTkcNixDhzZlb/JlZufi/N1nOHPzMZLTMtFWQwXTTE0wsl9PSEtJVtmHomIuouKTEZOYirjkdMQmpyE5PQu5+QXIzitAfmERJMTEIC0lDhlJCTRtVB9tVJuhrWoztFJRgoS48DnT3Tx8sMz+MERFOTi+ZTk6txX+huWuIy5wdrmKU7ttYdS9S5X1B02YgWZKTXBq385K63G5XHQzNIGxYW/ssd8qdH+Y2sPm2Jn/Cy4XXLFxmz22b9qAiePG1KgN59PnsevAMYweOhA7bVeXW7OdlpGFZZsd8MrjM0YPMsaWFX+UCdT5BYVwuf0UBy/cRnZuHvrodcTcCUPRS7d9hfPKSWmZCIj4hi9h3+AfFo2QmARExSeDy/t7wwuxeqJQrC8PWWlJyEpLQkpCHIXFXOQXFCI3vxBxKekoKuYCAMTF6sFYTxvDenVBf4OOkJGqegVM+Ld4zFy7CykZmdi/fjH6dRPuoa3ComIMn2mF/IJCPHTZV+VSzvV2Drj98Ck+Pbtd5XJTa9stuH3vPt48ewQFIda/M7XrlwZ2DodzEsBwAElEVOWjbCyw/zfk5ObCaMAwtNduizPHnGt089H15j2s3boLpoNNsGfT2nJBPTAkAnNWb0VqRiZsLedikunA0vMUc7m4ePcFDl68heS0TBh17YSVsyZAu5VqmTaICKExCfjgH4qPAaH4GBCG+JSM0nI1ZUW0UW0GTZWmaNVCCWrKimim2ACKDeQrTc7F5fEQGZeMoKg4eAaE4eFbbySmZUJSXAzjTLpj4fhBUGpUeXKz5LQMzF6/B4Fh0di8ZDomD+sn1Pvm5ReI8X+swYJp47Bi3rRK6956+BRL12/F7XNH0aFt60rrBgZ9xfCxk7B08QIsmj9XqL4wtedXB3ZDADkAzrLAzvzl8LGT2OW0HzcunatRyl23Nx8wd9la9DLQwzFHu3K7Gj178xGWG3dDQU4GR+zWlZl6+RwQinV7TyIoPAYGHdtg2czxMOjYprScx+Pj09cIPP3gh8fvfRAZnwwAaNpQAV3ba6JLG3Voa6ignVozyMvWzo5EfD4fnoHhuPb8A64//wARERFMGdwbf4wdgCYNFSo8Lje/AIu3HoCbhw8WTx0Fq+ljhPqQXLrZAQ/d3uHZxUNo1rTideqx8QnoM2ISNq5cAvOJVX+rmrfICh+9PuPl47uQk5Orsj5Te375qhgAagD8hanLbp7WfWnp6aTb3ZBmzltYo+P9A4Opfe9BNHzKHMrOyS1Xfu7GfdLsM4pGzFpKicmpf583M4vW7DlO6iZm1GPSYnro/rHMDdHgqDiyO3WDuk23JrURC0lr9BIytzlA5+6/oqj45F928zQmIYVW7TtHmiMXU/sJy+jkrefE5fIqrF9UXEwrdx0tXTFTzC1/U/h73+KTqE3fsWS942Cl9fh8PvUcOo4WrdkoVN/9vgSQhrYOOe4/JFR9pvbgV6+KqSqwA7AA4AnAs2XLlj/9DWB+L9utdtSqQxcK+hpc7WO/xcWTwcDR1HPoeEpISi5Txufzae/Ji6Tey5Rmr9xSZlnfay9/6jZhEWkNmk7bDp+n7Ny80mOeefjR2JV7SG3EQtIcuZhmb3GmO688KTO7/IfGrxQRm0TTbQ+S2oiFNGKpPfmFRldYl8/n064Tl0ndxIzm2TpSQWHVyyHX2O+ntn3HUVpGZqX1llhvJoOBo4X+YFtotYI66PWg5OQUoeoztUPYwF5rN085HI4agLvEpmL+867dvI01GzZh8vix2GxjXa1jc/PyMHbmQsQnJuHKiQNoraleptzxxAXsP+WKsUP6wW71ItSrJwouj4e9Z6/j0MU70GihjL3WC6DdShU8Hh93X3vhyPWnCIyIRfMmDTFjuBFGGnWFYoO/b/wREWJTMhCfmonEtGwkpWchO68APD6B/+e/DzlpSchLS0JBVgpN6suhuWJ9NGkgB9EabIDxPSLCvdefsOnYVaRl5WDRhMFYPHEw6lWQ2Ov0jUfY4nwevbt0wNHNVpU+ARscHo3B5ouxar455puNrbDehWu3sd7OAU+vuUBDVaXKPkdERmGQ6VhMnTQettarq75IplawJGDML0dEcD52Env2HkDP7gZYtdyy2sev2rQDoRFROLVvZ7mgfsjlKvafcsX4YSawW70QIiIiSMvMxqIt+/HeJxDjBhli48JpkJaShE9IFGycXeEbGo1WKkrYuWQqRhkbQKyeKPh8Pj4GReKldwj8wmLhFx6L9Ow8gX0SFREB0d8B/vuyZo0VoKrUCGpKDaGq1Ajqyo2h2VwRLRTrVxiYv8fhcDC8jx4Mddth8/Fr2HfpAdw/B8Jx2XSoKpefG58xehBkpKSwxuE45m/ci8MbLSsM7q01WqJrZ21cvvsU86ZWPDffXV8XAPDe87NQgV1dTRVjR43ApSvXMXeGeY03F2d+DjZiZ2pFdMw37HTYiwePn2Lk8KGw37IR4tVYtw0AjodPYv/xs1izZD4szCeVKTt95Q427z2OkQONsHudJURFRRGbmIJpq3cgLikV25fOwpgBvZGVk4ddLndw/uFrNK4vB+uZo2FqqAcOhwPPr1G4/doXTz4GIDE9G6IiItBSaYJOms3RSaM5VJo2RNMG8mjaUA7y0pKlK16ICHmFRcjMyUdGTj6S0rMQl5KJ2JQMfEtKR2RCKiITUpGVW1DaXzFRUbRqoYiOGs3RUbM5OrdqgfZqykJtcXfX3QvWhy6Bz+fDbuFkjDAUPEBzfeCGtQ4n0L+7Lg5vtIKoqOC2rz94jhXb9uLSwe0V5m8nIvQaNh56nTtiv51tlX0EgLi4eAw0HYO+RobYv2eHUMcwP+aXjtg5HM5FAMYAGnM4nG8AbInoRG20zfx/i42Lw8EjJ3DtZska6OWWizB/zsxq79HpdOQU9h8/i/GmQzF32sQyZVfvP8Pmvccx0LA7dlmXBPXwmHhMW22P3PwCnNu5BvodWsMvNBoL7E8gLiUNM4YbYenUYZCRlMBTzyA433oF75AYSEmIwahzawzu3h79urSBnHTVDyZxOBzISEpARlICzRrXh7aa4NFpenYewuOSER6XgrDYZARGJeCJZyAuv/ACADRSkIGxTmsY67ZBvy5tIC0peJQ9vI8edNuqw2r3aSzZfRpBkXFYbja83Hs6cYgxCouKsfHAWWw7cgE2CwQn8hps3BMb9hzGnSfuFQZ2DoeD7nq6cP/gWTJHK8Sqm2bNlDF96mQcPXkG32Lj0KJ5zXLZMz+BMBPxtf3DVsX8u3G5XHr99h2ttLahNp30qW3nrrRxmz0lJFY/vwqfz6c9h46Tup4RrdxoTzxe2ZUhD93ekmafUTTNyoYKCkvSCASFR5P+uD9If9wfFBAaSUREV5++o9ZjLKnnzPX0KTCciIje+YeRiZUjqY23JsNFu8nl0XvK+y7/SmZuAX2JSqRnn0PphXcovQ+MJr+IeErOzKnJWyPw+mKS0uj6y8+0xOkSdZ6xhdTGW1PnGVvI/txDSkit+KZmYVExrT1wgdRGLKTZW5wpN79AYL1NB86SuokZ3X/lUWFbizbsIL1hZgJTLPzF9eY9Utczoq+h4UJfX2xcPGl11CP73U5CH8PUHIS8ecrm2BmhEBH8AwJx4/Zd3HvwGCmpqZCVkcGEsaPxh8VsKCs1rXabhYWFsNmxF1du38eEkUOxfd2KMqNSD58vsNy0B53baeHw9rWQEBdDxLcETFu9A6Iioriw2xrqLZSw+9wdHLz8CL06t8G+lTMhKS6OjSfv4szDd1BTaoR9lhMxpHt71BMVRVxqFq6/+YLn3mHwDPmGrLzCCvvXorECdDSV0aVVcwzSa41mjar/pCWHw0ELxQZoodgAow11wOXx4BkUhbOPPuDobXecuPsGY411sXLyQDSUL5uuV1ysHrYtmIS2as2w6dhVmG3Yj9MbF0Jepuym3GssJsMrIAQ2+06hW6e2aKhQfm35EONeuPf8DT59Capw1G7QpWTTak9vv3L3NyrSTFkJ+l108eEjm1r9f8JSCjCViouLx50Hj3Dj9l2EhIZBXFwcfQ17w3TYEBgb9oakZNVTGYJ8DQ3HMpttCAwOw6LZ07B0/qwyX//9v4bBzHIDGjesjyvO9migII/YxBRMWLoVRcVFuLh7HTRbNoPtkStwuf8Kkwb2xOb5ExEQGQ+rfZcRmZCKGUN6YNWUgZAUF8NL33Dsu/UWn8PiAAAqigro3V4Nak0boIWiApQbygNEyCssRm5hMaIS0+EdFgfv8HjEpWaBwwEM2qhgal8dDDNoBxGRH0/hG52YhuN3X+Pi04+QlZLAOvOhGGukK3Aa5NE7HyzedRLtNVRwbsvicikJgiJiMHLBBgwz6g6HNfPLHZ+dmwe9oWaYNXEk1iyYLrA/RISuA0ahb58e2GUrfM71jdvscePWXXh/cP9pqY2ZEixtL1NjOTm5dO3mbZoyYy5paOuQhrYOjZ08jc67XqGMKtZDVyU3L492Hzy8TfW8AAAgAElEQVRGWgb9SK+/KT13f1euzhtPH+o4YCL1HjuHYuJKshumZWaRycxV1HmURen0i92pG6Q2YiFtO3md+Hw+vfIJoXZmttRrwU5696VkOuFTaCxN3H6e1Mztqc9yZ3K++55CYqv3IFJEQhrtvfGajFceITVzexq58Qz5hMf90PvwT0FRCTRuwxFSG29Nc3e4UGaO4HTEj955k+bIxTR365FyU1ZERHtOXSF1EzPyDgoTePyUJetpkNmiSvsyY/EqGjJpVrX6v+/QEdLQ1hFqXT3zY8DS9jLVFRefQNt3OVAng96koa1DxoOG075DRyg65tsPt11QWEjnrtwkg4GjSV3PiJbbbKfU9PRy9e6/eENtjMfQILNFFJ9U8vBLdm4ejVm8kdoMmUkffIOIiOjQlUekNmIhrXe+RHw+n+6/8yOtSRto8Ip9lJSeRcVcHm2/9JzUzO1Jb9E+OvPEiwormV8WBo/Hp6vufqS/eD+pT7entScfUGaOcHnPq26bR8fuuJPWpA00cJkTfUsu/94QEZ2684LURiykHadvlivLzs0jvbF/0LRV9gKPPXr+Oqn3MqW4xGSB5URE2xwPUtueA4grxJOtf9m4zZ46d+stdH2m5oQN7GyOnUF4RCQOHjmOuw8egYgweGB/TJs8EfpdBE8LVEduXh4u37qP4+dcEZ+YDH2djji4YxP0dTqWqVdUXIz9p1xxyOUqunRog2M71qO+vByycvMwy3oXfL+G48CGxTDo2AZXnr7DzrO3YWqoh00W4/HEMxCLnVzRuVULnFxjDlFREcx1ugY333BM7auDNRONIfvn1AWPz4d3RBKe+UYhICYFoiIc1BMVgXg9UfTRVsFwfU1ISwhepikiwsHY3h0woIsW9t54jTNPvRAUk4zTy8dDXqZmU1J/ty2COcN7o71aM8zbfR5TN53A5c1z0aRB2Xn96cOMEBIdD+drT9C9U2sY6rYrLZOVlsL8icOx/ehFfA4Iha52qzLH9ummC7tDp+Hu4Y0Jw00E9kNNpQUKC4uQlJIK5aZNhOp7ZFQ0lJWUqnnFzM/E5tj/w5KTU7DP+Qhcr96AhLg4Jo4bgxnTptTKsrXk1DScdb2Oc1dvITMrG/o6HbFo9jT06d613IdFYGgkVmx1QmBoBMYO7Ycty+dDUkICWTm5mL52J76ERGHfuoUY3KcrnnzwxR92x9GjU2uc2DAfn0NiYL7tNNqpKuHchlnILSjCLIer+PotGZvNB2JK35JUt+k5BXC644m7nqFIyymAqAgHbZs3AocDcPmErNxCxKXnQE5SHCO7aWFGvw7QVKp8L9ZHnsFYfOgWWjVvjDMrJkBRoXp7lVbEOzQGZptPorlifVzaOBcN5MomISssKsYQSzsQn/Bwv3WZPO85efnoOXkJ+nXXhdPaBWWOIyIYjJiOPt104bBhqcBzP3z+CgtW2eDu+WPQbqNVZV8LCgrQpacxJo0fA5u1q2pwtUx1sDl2pkJcLpeOnTpDHfV7UutO+mS71Y6SU1KrPlAIYRFRtHbrLmrTw4Q09I1p3or15OXjL7BuZlY22R08RVqGo6nrCHN64v6+tCwmPomGzVtHrQdPp8dvPImI6J1fMLUZa0Wmy3ZSTl4BhcYmUacZm6m/lSOlZeVSRk4+9V99lNpbONAL79DStp54R5De8tOkOf8wLTn2hO54hFBmbtmlg3w+nzxC4mjpyWfUesFRarvwGHlHVL180803jNrN2UPjtrjUagKxt35h1HqKDc3d4SKw/LV3EKmNWEiHrz0pV7bpoAu1HjydUjOyypUtttlJPUbNrPC87z5+InU9I3rj4SVUPx89fU4a2jr00v2NUPWZHwM2x84IEhoWTmMnTyMNbR2a88cSCo+MrJV2P/n607zl60hD35ja9DAh6227KSxScEKrgoJCOnbhBukMnkLqvUxpxTYnSk3/+6bso9cfqfMoC+poOpfcPEr2R/UJjqQOE5aTyYItlJqZTamZOWS0aDfpzdlGMYlpVFjMpUnbL5DWzJ30LjCq5DxFxbT67AtSs3CmwZsv05foiueW/ykxI4f6WJ+jrivOUGxqdpX1zz71IjVze3oXECVU+8I6cO0FqY23po+Bgn9HU9btpe4z1lFhUXGZ1/1DIkjdxIwu3H1W7pjTV+5UOs/+8bMvqesZ0at3Fa+J/6cZFguoh/EAKi4urroy88OEDew/nsGI+VcgIpw5fxEjxk1GRGQ0HHdsx9GDTlBXVa364EoEfA2B+cIVGDtzITw++2LR7Gl4ffcytlkvL5dzhMvl4cq9p+g/ZQG2HzyFzu20cOekI3ZZW6JhfXnk5RfAZt9pzN+4Fy2Vm+KO8xYYde2E195BMLM5gPpyMnDZvAgykhKYt+s8EtKycGylGZor1sf604/wPigaO2YPRfe2LVHM42H+4Ue4/CYI8wfp4OaaMdBWaSzUNTVRkMGJhUNQUMTFH0cegc+vfLpyQp9OaKwgg6MPPtT4fRRk5tCeaNJADo6XnwosnzOqPxJSM/D4vU+Z17U1VaHWXAn3X3mUO0anfUlOeu+AYIFt/jVNRkJM0UZGRePV67eYNH5slTsvMb8W+238B2Tn5GDN+o14+OQZ+hr1gd0mGygqChfkKhKfmAQH5xO4fu8xFOTlYG21AFPGjoC0lFS5unw+Hw9fvoPj8QsIi/qGjm1bwX7NIvTuWjL/TUS46/Ye9scuISElHbPGDsbKWRMgIS6Gc/fdsfHoFbRSaYoTNn+goYIsFuy5CM+vUdhvNQm6rVvi8L0PuOLuhyUje2J0r/bg8wkrT7vBzT8G26YaYoqhdrWvT6tZQ9hO6oUVp1/gqW8kBupU/MCOhHg9jOzeDi7PP6OgqBiS1cyRUxFpSXFM7KePg9fdkJmTDwXZsu+tUZd2aKQgh6cefhjeR6/0dQ6Hg37ddXD+zjMUFXMhLvb3P/M2Gi3B4XAQHB6NIcY9y52zqLgYACAuVvU1XL15GyIiIpg4bnRNL5H5SdiIvY4LCQ3D6IlmePLcDWtXLsWxg3t/KKhzuVwcOnUe/cdMw51HzzHXbCLcbp7HHLMJAoO6T0AwRlusxKINOyHC4cB52xrcPLa7NKj7h0Ri0vJtsNx+CI3qy+Oy43qsnz8VRIQNh12x4bArjLq0w9Udy6HYQB6Wey/jmVcQtswxxfCeHfHYKxg7r7hhmEFbWI7qDSLC1itvccsjBCtHGdQoqP9lpIEWWjaWx8H7n6ocwfbUVkNRMQ8fgmJqfD5BjHS0wCfCa7/QcmUiIiLoo9sW7p+DwOfzy5R17dAGhUXF8P0aXuZ1SQkJtGzWFKGR0QLPl5efDwCQEvC7/Cc+n4+bt++hT68eaNpEuNUzzK/DRux12IuX7rBauRYSkhJwOXEY3bpWfTO9MmGRUVi1aQc++wVgcD9DWFv9gRYVpGvNysnFnqPncO7GAyg2rI/d6ywxcqBR6Z6lCSlp2HPyCq4/fYMG8rLYZjUTEwYbQ1RUBO/9Q7D2wAVExiVjzqh+WDN9FIq4XFjsPIeX3iGwmTEMZgO74XNYHCwP30EndWXsnjsUIiIcHH70Gaee+2Fmv474Y7BumT5xeXxEJGcjJCETwQmZ4PII5n200ERecBCrJyqCeYN0sO78K3wMTYCBVsWpaXtqt4Siggz23XoDw47qtfYEZqvmJUEzMS1LYHmnVi1x0+0jMnPy0EBetvT1DlpqAIDQ6Fjodyi7j2kL5aaIS0wR2F5Obkn6YlmZygP7Zx9fxCckYOXSxUJdB/NrscBeR50+dwHbduxBu7ZtcGS/Y41yufyFx+PhmIsrnI6egpSkJPZu24ARg/pXWP/Vh09YbbcfSanpMB87FMvmmkFOpmTJXmFREY643sORy3fB4/Exd/wQLJhsCnlZGWTl5MH+zC1cfPQGLZUa49yWxejVuQ3iUjKwyPESvEO/wW7eKEzq3xVRiemY63gNigoyOL50LCTFxeDmH42dNz5guL4m1o/vWSa4fo5MweKzb/EtLRcAwOEAHHBw8uVXzOvXDvP6t4OkWPn86aO7a8H++nu4uPlXGtglxcWwbEwfrD31EPc/fsUwg7Y1fbvLKObxAKDC3O5/BfO0rNwygb1p4wYQFRFBXFJquWMaN6yPT35BAtvLzCz5AFGQrzwvzsPHTyEuJoZ+xoZVXwTzy7HAXscQEfbsPQDnYydh0s8Yjju2Q1q68tFXZZJTUrHMZjveeHhhcD9DbFptBcVGDQXW5fP5OHj2CpxOXISWeksctrNG53Z/r4X2+hKMNXtOICwmDkMNDbB6zkSoKDcBn8/HpcdvsevsbWTk5GLOqH5YNnU4pCTE8fhjAFYdug4uj4dDyyZjcLf2iE3NwtSdl8Anwqnl49FYXgbBcWlYcuwp2jZvhJ3TjUtzufD4fBx6GgCnh/5QUpDGrsnd0K5ZfWg2lUdiZj523vWB40M/3PSKxJFZfdBaueym0lLiYpjQqy1OP/dDTEoWVBpXHPDGG3aEy7NPWHf6ETqoNoVq08rXwQsjIr5kZN24vqzA8r82APl+qqieqChkZaSQlVN+AxFZaWnk5AneWCQtIxMAoCBf+SbVL169RvduXSEnK7hfzO/FAnsdwufzsWHzdly6cg2Txo/F5g1rS6c+auLekxewsXdEfkEh7NavwISRwyqcYsjOzcPyLY54+toDowYZY9vKBZCSLHnas6CwCLtOXsbpG4+hrNgQp7evhGHXkkyC3sGRsD18Gb6h0dBvp4GNFuPRXlMF+YVFsD15B2cfvkcH9WbYZzUR6sqNERqXAvNdl5GTX4jzqydDU7kRUrLyMfvAA0iK18PxhUMg9efNy/TcQsw74Q6P8GSYdlHFlnH6UJD+Owe6mqIcDs3sDfev8Vh67j0sTrzCrWWDytQBgDkmneDi5o/Dj7yxbWrFI1RREREcWjQKIzedxbx913F1vVnpE6819fD9F4jXE4VhZ8EPC4VEx0OsnqjAnZbyCwpLfwf/xOPxKlzFkpSSikYNG0CsklUu8QmJiIiMwuTxFW+1x/xeLLDXEUQE2612uHTlGv6wmI3lSxbWeJ43NT0DtjuccP+pGzppt8XuTWvRSr3iZZGxCUmYvXILwqNjYWs1F+Zj//4AiE1MwTxbJwSERcFsRH+smjMRstJSKCwqhsP5ezh+6xka15eD47LpGGmkDw6HA3ffUKw7ehMxSemYObQnVk8dBAmxevgQFIN5+65DrJ4oLq2dAm3VpsgrLMbcQw+QkpWPSytM0axhyQgyv4iLWUdf4ktsOhymdsdofbUK348+bZRxeGZvTDrwDGtdPXBwRq8ydZUayGJCr7ZwfR2EeQN10FKx4lG7atMGOLBwJKbvuowZu6/gxLJxUKhhuoGsvALcdPeGkU5rgR8QRIQ3PkHQUlGGWL2yH+CpGVkoKuaWmZ75S05ePqQkBH/gxCcmQamKm+sfvT4BALoZ/Ng9G+bnYati6ojdTvtxwfUq5s2egRWWi2oU1IkItx4+xeAJM/DE7TWWL5iDqycPVBrUfYNCMGbeKsQnp+K0w0ZMHze89NzvfQIxcqENYhKScWLrcmxeMgOy0lLwDo7EMCt7HL3xFBMH9MTTQxswyrgrMnPzseLgVZhvPQVRURFc3DgHNjOGQUKsHm68+QLzXa5oJC+Na+vNoK3aFMU8HhYfewLfyGTsndMfndVKbjRyeXwsPvMWPtFp2GfeE2O6Vn0zU19DESuGdcJ9nxhcfBdWrnzRUD2Iiohg963ya8O/17u9Gg4sHAnfiHhMsruA5IycKo8R5NB1N6Tn5GPJuL4Cyz2+hMEvNAZTBvcqV/b28xcAQLdO5ef6QyNjoKHaXGCbIeFR0Kzk9w0Afv5fICEhgbatq045wPwmwjzFVNs/7MnT2nX2/CXS0Nah9Zu21vix9q+h4TRlnhWp6xnR6OnzKShEcOrXf3r53ou0+4+nPuPmUHB42acu77x4R1qDppPJzFUUFvN3itszd91Ic+Ri6jlzPb38FFD6+otPQdR17nZqNWk97bzwqHS3pPzCIlpz4gGpmdvTxO3nKT27JKUtn8+nFaeek5qFM51/+aXMuTdc+UiqlhforHtwtd4DHo9PZoeeU+sVrhSdUv6J0903P5CahTP5CJFqgIjolV84tZuzh4ZtOFXtzJJ+Yd9Ia9IGWn7gisDyYi6Xxq3aQ7pTVpXbFYqIaJ6tI+mMnkdcbtn0vlk5udTaaAzZHTxd7pj0jExS1zOiAycEpzH4ywSzmTR2ink1roapLWApBf4b3n34SFod9WjOH0uqlWr1L3n5+WTn5EytDPqSTt/hdPbyjSrb4fP5dOrybWplOIqGmC+hpJS0MuUX7j4jjQHTaMLSLZSZk0tEJYFog7Nr6TZvf+UczysopPXHbpHaeGsatGwvfYmILW0nLD6Vhqw/SWrm9rTD1Y2K/xGk7K6+IzULZ3K6/bHMuc+9DiFVywu07eanar8XRERx6bnUdqUrzT/pXq4sK6+Quiw7RaPtrhNXQD50QR57BZOauT3ZXXohdB+y8wrIePEe6j7PnlIr2KLP4fxdUhuxkK4//1Cu7INvEKmbmNE+lxvlys7feEDqvUzJ+8vXcmW3HjwldT0j+uQrOLcPEVFRURFpd+lOW+13CX09TO1hgf0/IC4+gfR7GdOA4aMpK7vqnCbfc3vzngxNJ5G6nhGt2rRDYH707xUUFNKKbU6k3suULNZso+zc3DLlJ689JHUTM5ppvYvy/tyjs6CoiOZsOVy6KcZfo8hvyek0YKkTqY23pi1n7pWO0omIHnwMog4WDqS7YG+ZhF5ERIcffiY1C2daf/5VmW8oYYmZpLX8Epk7vxA68Ari+MCXVC0vUHB8RrmyG++/kpqFM7m4VRz8vrf25ANSn25PkQlpVVcmIqt9l0ljwjr6EBAhsPzJB1/SGLmIljmcKVeWm5dPQyzWUo9Ji0vf/78UF3NpsPliGmy+WOA3u4WrbUmvv2mlH+zePn6koa1Ddx88EupamNrFAnsdV1RURGOnmFNH/Z4UFh5RrWOzsnPIav0WUtczov5jzOjdR+FGt+HRsWQ6exmp9zIlh2Pnyu3ic+bmY1I3MaP5G52o6M+kUIVFxTRrszOpjVhIZ+66ldYNjIqnbhZ21HH6ZnrlE1L6OpfHo52X3Up3KopNKbtjk+vrQFKzcKZFRx+XC95zjr0k7VWXKTFT8A5EwopLzyVVywt07EVguTI+n09jd1ynXmtdqEjIb0ghscmkZm5PV919q6x7y92b1MZbk9PlpwLLX3sHUesxlqUZLv+pmMul2et3k8aAafTs/edyxx447UrqvUzp3rPX5fsYHkmaXfuSnZNzpf3bsceJWnfSpzQhBgFM7fulgR3AYABfAYQCWFNVfRbYf9wWu101Gjn5BwaTkelkamXQl5yOnBJqO7PiYi4dPX+d2vYdR50HTabHr96Xq3P21hNSNzGjuRscSrMNcrk8+sPuOKmNWEgu916V1vUOiaFOMzZTNws7CoyKL309r6CIZuy+TGrm9rTmxAMq+C5r4TPfSNKYd5imOd0pN2ftEZZEqpYX6MBj4UfSlTHccpvmHHspsOyJdwSpWTjTrQ/CzeFzeTxqb+FANmcfV1ovJimNOk7fTGPXH6ZiAR8aHl9Cqd24pTRo0VZKzyo7RVPM5dKKnUdI3cSMXG6XT+X74bM/aRmOpkUbdpQr4/P5NG/FeurQZ3Cl39r4fD6ZDBtF5nPmV3odzM8jbGD/4eWOHA5HFMBBAAMAfAPwkcPh3CaigB9tmxHs8rUbOOVyHtPNJmPY4IFCH3f97iOss9uDBgryuHhkb7ldjAT57P8VG/Y4IyAkAia9DbBlxXw0bdyotJyIsP/cTTidvQ6THl2wf/2i0qRTO87ewoO3n7Fu1miYDe0DAIhMSMUsuzNQkJHCBdvZaKFY8hBPYREXc/dew7uAaGydPhBT+5VNBxCdnAWrE8+grdIIh+cPgvh3y/uuf4yAjEQ9zDJqI/T7URlJMVHwKsjq2K+jKiTEROEfnQJTg6pXhohwOBAR4ZQ+TCQIl8eD1b7LABEcFo0v96TpB/9QzNp8CMqNG8Bl82LUl/t7U4+CwiJYbj+IJ28/wcp8DMxGlN0d6cNnf8xetQUtmyth64qym28AwIVrt/H4hTtWLJyLhvXrV9jHV6/fIjwiEhazBG+GzfwfESb6V/YDoAeAR//481oAays7ho3Ya+7mnXvUqkMXMp8zn4qKiqo+4E8Hjp8ldT0jmmxhScmpVc/1xsQl0GKbXaTey5S6j5xBD9zelpuX5fF4tOnAWVI3MaPlO8qOMi8+ekNqIxbSBmfX0uOycvOpn6UD6czcQmGxf+cD5/J4NMvhCqlPt6drr/3K9SUnv4gGbXKlzlYnKTq5/GbafD6fDGxuCLzhWRN5hcWksfQi7brrU2GdbqvO0KozL4RqLzE9m9TM7en0Y88K6zi6PiW18dZ0y927XNmnwHBqP2EZmSzYQklpZa8/IyuHJizdQhoDptHpG+W/vb3y+Eza/cfTgKkLyt3kJiLy9PajNt1NaMbiVQI3yP4Ll8ulMZOmUR+TIVRYKPzfO6Z24RfuedocwD9T2n0D0O37ShwOxwKABQC0bNmyFk7738LlcrHb6QCOnToDA/0ucN7rADEhUqsCwP7jZ+F4+CRGDx0Ie5tVlT5VmJ2bh4NnLuP0lTsQERHB4pkTYTF5NGS+S0uQk5ePNXuO4/4rD8wcMwjr5k2BiEjJYxEfA8Jge/gyDHXbwWbu2NI15NtdHiAyPhXnbWZBo9nfD8Ece+CB595h2DRtAMb06lCuT4cefsLX2DScsRwm8JH+Qi4fiZn5aKtc8WhTWEQEm6ue4PEJvVoLzq/jH52M5Mx8NJITLlXDVXc/AIBuK8FbDr4PiMD+ay8w2lAHpr07lyn7EhaD6ZsOQbG+PM5vWQzFf+yBGpuYglnrdiMqLhF7rRdguHH3Mtdx+spdbD94Eq3UVODitBmNG5R9f9zefMDC1bZQaqIIh83Wpb+/7xGVPPzm7euHnds2QbyW0hIzP5Ew0b+yHwDjARz/x5+nAdhf2TFsxF49fl8CaPL0OaShrUMbNm2r1ojpwAkXUtczohW22ysdkfH5fLpy7yl1HWFOGr1H0optThSflCKwru/XcDI2X06aA6fREde7ZUbykXFJpDtlFfWdv6nMPPArnxBSG29Ndi4PyrQVGJ1ErWftovn7rgtcqfEtNYvaLDxKlscF30z8i671NVpzqfzSv+rg8ni0+boXqVpeoD33BI/WC4u5ZLr9KumvOF1uez1BEtOzqb2FA811uiawPDUzh7rPsyfjJXso+7ubocFRcdRl6mrqOWs9fUsqu3Xhl5BI6jZhEXUaaUHvvAPKlP1z5dI8ASuXiIguXr9DrQz60vApcygpWfDvmajk78VOh72koa1Duxz3VXm9zM+FX3XzFGwq5qdIS0+ny9du0KgJU0lDW4c6d+tNV67fqlYbLldukrqeEVmt31LpErbIb3E0ceFaUu9lSmPnrSSfQME3BblcHh2+dIdaD55OPScvoQ++QWXKM7Nzqf8fm0lnykqKiE0qfb2Yy6V+lg7Ud4lDmSWNREQWTtdId8FeSsksH3yIiPbe+Ujq85zpW2r5/Tv/aeL+p6RjfZVCE8pP1QjDIyyJhu56QKqWF8jm6keBHzJfopNp8ObLpGbhTLc9QgS0UlZ6dh4N23CKWs/eRRECljoWFBXTRNtj1HryBvIPjy1TFh2fTAbT11JX87UUHlv2gagPvkHU0XQO9ZxsSV8jYsqUxSUm08g5y0m9lyk5Hr9Q7sM8JzeXVthuJ3U9I5q+aAVl5wh+34mICgoKaMXaDaShrUPrNm6p1T1dmZr5lYG9HoBwAOoAxAH4AGhf2TEssJeXmpZGz91ekd0uRxoxdhJpttclDW0dGjRiDJ1yOU+ZmZUHtu89fP6KNPSNabbVmkr3o7z1+CV1HDCROg+aTK53nlQ4qvf6EkzD5q0jdRMzWrBpL6Vnll03X1TMpanr95HW6CX0zq/sB8NVt0+kNt6aHrwvu2IlIyeftGbupC3nKx6Nzz/8iIzXn6/qcikiKYv01l2jnhtvUVx6xcHqnwqKuXTLK5JGOz4mVcsL1N32Jt32iiwXwIq5PDr04BNp/XGE9FecpsfeEVW2nfaPoP79OnyikpGw5V5XUhtvTTe/m1dPSssko7m21HnySgqKLBvw3b38qN2wWWQycxXFfTeK9w4IJgPT6dRxwESBK5cCgkOp/xgz0tA3JsfDJyv9e5GUlFy6N67TAedKv+0xv46wgf2H59iJiMvhcBYBeARAFMBJIvryo+3WZVwuF4Ffg+Hx0Quen73h5x+A+IQEAIBYvXrQ1ekEywXz0LtXD+h06ljtvC++AUGwWr8Fndu3xX47W4GZ/Ph8PnYePoujF25Ar2M7ONkuR3Ol8hkCM7NzseP4JVy67walxg1wYP0iDDE0KNOnomIuljmexRufr9hlaYbuHbTKnOfA9RfQVlPGwK7tyrT9JiASxTw+hlaSuzwmOQvKDapODaumKIdT84wx6cAz9Nh4C33aKKFPGyV0b9UE0uL1wCMCj0+ITs3Bl2/p8P+WDs/wZGQXFEO1sSw2jNLFpB6akJH4e/44M7cQF90DcNbNH/HpuRjSRQNbp/ZBQ9mK59YLi7lwfemLg3feISM3H0eXjIFRJ40ydfh8Pjaeuotbr32wYtIAjPzHvHp6Vg6m2RxAckYWzm1ejDaqf8/Lv/roCwtbJ2ioKOGs/Wo0bvB3iuEX7zyxcP0ONG5YHy6Om9Fao+x9rKt3HmCDvSMU5ORw3tkB3fXLrjr6CxHh9r0H2GK3CwWFBTjgsBNDBg2o8v1n/r/USnZHIroP4H5ttFVXcblcvH73Hjdu3YWb+xvk5JQkhmqpogL9Ljro0L4dOmhro1OH9j+UPz0pJQ/0PRwAACAASURBVBXzV6xH44YNcNRhO6Qky2cW5HJ5WL7VCXeevsLUUUNgazUX9b5bPkhEuP3iHbY6n0dGVg5mjx0CS/PRkP2ubwWFRViw4wReeH6B9czRGNe/e5nyd18iEBmfCsfF48vdnMvMLQAAKDesOPe3fislXHodiJyCIshKildYDwA6qjTEg5VDcNo9GO5f47H9trfAeiIcDrSU5DGkswqG6bREnzZKpfnbASA8MQOnnvnh2ruvyC/iolfb5tg61RB9O7Ss8EM2r7AIN98G4ODtt4hLy0bX1i1weNJo6GqWvWHK5fGw/thtuD73xNwRvbFgtFFpWVZOHsxtDyIiLgknbf6Abtu/91l9/ckfFrZOaNWyGVx2rkaDf+RLv/nYDSu37UU7TXWc3GNT5iZpYWEhNu3ej0s37qKHvi6ctm2oMJ9+UnIyNmzahqcvXv6vvbuOqir7Ajj+vQYWKgrYASpYiAF2t441dusYY4w6dmF3d3fH2Drq2IWNgUhISqOE0vXgnd8f6vzG4VGKg+D5rMVaw7xz79s8Yb/7zt1nH6qZVmHJgjkYlyubxCsufa9k295vLD4+nv2H/2Dnnn28eeuPTv78tGvTirq1a1LTrAZFCqfdfpHhEZEMnziT0LBwju/ehF7BhBs9CCGwWL6JP6/dYdLw/ozs1zVBsgoKDmXqqh3ceGhN1Qpl2LdkCpXKJez4FxIeybBF27Gyd2XRb73o06ZBgjHHbjwhf55ctK1dOcFjMaqPuwMlUo0B0N68LPtu2nLgll2Cre40KaWnzezONQB4ExzJM/dA4tWCLFkUsioKhfPnokIxHXJpff6rHxGt4tJzN07cd+Shky9a2bLQqZYRg5qbUrGErqanwjswBEvb19x84cY9O3ciY1RUL1uMZUN/on6l0gleV//3oUzYeIJ7L10Z3aUJE3q2+HvMu9BwBs3djKOHL9sshlG/6v/r8R++cGDY7DWUKVkkQVI/fekmkxato051E7Yusfh7pyqA4JBQBo+dirWtAyMH9WX88EEaP70JITh+6gxLVq4hJiaW6ZPHM6h/36/q5S+lL5nYv6HXHh5MtpjNc2sb6tSqyWyLqTRt1PCblItFRkUxZNw0bF85snnZfCoaab7SOnDqIicuXmfMLz34rX+3BI/bOrszbPZq3oWEMXNkXwZ2akXWrAkTr72bN2NW7MHrbSDrJg6kQ6OEvbnj4uO5Ze1Em1qVyaHhZ65Q8sPUzxNnH9rW1LywyKxsEVpXM2TFmUcU0clD5zrGGsdpUkQnNz9VS7y0NkYVzx17L/60cuHaC3eiYuMwKJSPiZ1q0rNBRfTz5f5sfEBwOHftPHjg4MEDB0+8Az/sNlRMNx+d61WmQ51K1CpfQuNV/fWnr5iy+SSRMSqWjuhMz2b/f738At8zYM4mvN4GsWX6UJqa//9N8PFLR4bMXEnJIvrsX/p5Ur9y5yFTlqynbo0q7Fw+k5z/6LEe9D6YAaMm4vrak83L59OmmeYNQgICApk+Zz43b1tSu6Y5i+bOxNAg6ba90vdPJvZv5OqNm4ybbIGWVnbWLFtMh3Zt0myD43+LiY1l2MQZPH1hy9qFM2nZJOGVM3xYRbpw/S6a16/J2MG9Ezx+/7kdv85eTYF8eTm5fg6VyxkkGCOE4PClu8zfcZIC+fJwYP4YapuU0/h81s7ehEZE07i65mRsblSCAtq5OHnXljbmxhpfH0VRWDe0Ob+sv8iEPTd4/votY9ubp7iG/N+iY+O4Y+/F5eevuWbjTmhkLAXy5KRzHWM61zbCrGyRv+OIi1fz2NGLG9Yu3HfwxMHTHwCdPDmpXaEUQ9rUpF7FUhgV10v039bVJ4D1J25w7p4NFUsXYf3YnpQr8f9PaU6efgyat5mwiCj2zR312Wv5+KUjgy1WUExfj4Mrpn82p/7gmQ2/z1lBlfLl2LbE4rOkHhwSSt/h4/D08WPHmsU0rFNTY2y3LO8yefosIiKjmG0xhf69eyZayy5lLDKxfwOvHJ0YN9kC43Jl2bJ+dZpOt/xbfHw8k+cu5f7jZ6ycO532rZppHKdWq5m3bgd6BXVYNWt8gj9gV09fRs5bT8ki+hxYNg39ggkX+8SoVMzZdpw/rtyniVklVo0fQEENO/R84uT9FoCq5UpofDxb1iwMbm3OqpOWHL5pnaCNwCc5smdj7+/tWHziAQdv23H6oRNDWpjSoWY5yhTWSfINUwiB65tg7r/y4YGjD3fsvYiMiSNfbi1amBrQoWY56lcsTvaP0w5x8Wosbd24+PgV161deR8ehVb2rJiVK86U7o1paGJApVKFP5uT1/ize71ly5k7nLv7gpxa2RnVpQljujT57JPL+bvPmLr+IHly5eTIorFULlvy78duW9kwct46ihXS5dCK6ej/I6k7uLgzwmIppYsXZffK2Z8tHouJiWH4pJm4e/mwZ8Ny6iZyk/TQ0WPMWbiU8kblWLdyKeXKltE4TsqYZGJPY7GxKsZNsSCvtjbbN65FP5ltxr6Go4sbk+ctxdbBiSmjh9GlfetEx567egcbB2dWzBhLPu08nz0WGh7B0Fmr0MqejZ0LJmpM6qERUQyZv4UnDm781r0VE/q01zhF809vgkJRFIVCOonfHP2tfV2eufgw7+A1yhbVpU5FzVMnObJnZV7vBvRvUpkVZx6x7vxT1p1/Sim9fJiXK4JxsYLk1MpGzuxZCY+Oxcn3PR4BIbj4BRMUFgVAsYLadKplRJsaZahbvtjfyRzA/e17Dt14zpkH9gSGRJAvdw6aVStHazMjGlUxJHeOpG/cCiFw8w3kwoOXXHxgi6PXW3LlyM7QDg0Y1rEhuvn+/5qr4uJZtu8Mu87epEYFQzZNHUIR3f+/5udvPWTisq0YlS7B3iWTP7tS9/J9y6CJc8mdMwe7V85G5x9TM0IIZi5ZjdVzG9YtmpVoUt++ex/LVq2leZNGrFu5lFy5vvxmvfR9kok9jT2yeoKziysbVi//ZkldCMGhk+dYtGYT2nnysGHJHNq11Lx92id7T5zHuExpOrdukuCx/Wev4uHrz7E1syihoeRRrVYzYc0+rJ3c2TBlMO0b1EhRnDk+NgMLCg2nSMH8GsdkyaKwZngHuiw4wMCVx1g2pC0/10t4o/WTckULsG1kG7yDwrhl68nNl57ctvPi1EOnz8bp5s2JQaH8NDEpiXm5otQrX5ySenkTXN3bur9h8/mHXHriSNYsWWhWtSxdG5jQpGrZBI3GPhFC8OZdKE5eb7F77cdzZ0+eO3sRFBKBoiiYlS/FnEHtaV+vCnr5P/9E4+r9hklrD2Lt5M6Ado2YMbjL303ThBBs/eM8K3Ydo2aV8uxYMIF8/7gZ+iYgiH5jZxETq+LopsUUL/L5J8GT5y9x8vxlfv91IB1aN9cY+7nzf7Fs1VratW3FqiULU9yWQspYZGJPY5b3H6CVPTtNG2me5/5SsSoVNywfcO/xUx4/e4GzmzuN6tZkxdzpiZavfeLu7YeNgzPTfhuYYApGFRfHwXPXaWhWBXMTzXPhG49d5vpjW+YO657ipA7Qto4JK49e5fz9lwxtn/jrkT9PTk7M7MfIDacZv+08z1x8mdGrKTm0Ev/1LKGbl36NK9OvcWXUakFUbBzRqg9fObJlQy9f0lehz118WHvmHndeviZvLi1GtqvDgBY1KFwg4aeLkPAoHtm/5omjBy9cvHHweENYZPTfj5cppkeTasZUNypJM7MKFNVN+Camiotn26mrbDh6idy5tNg4ZTDt/vFaRsfEMnPdHk5dvUvHZnVZNnEoObT+/ykh8H0w/cfN5n1IKAfWLaB8mc9vcLp5eDF3+TrqmFVjzNABGn/mZ9YvmDpzDrVrmrFysUzqmZlM7GnMyckFo3Jlv/rjbUxMDLcfPMbGzpGXDo7Y2L8iJDQM7Ty5qWFamV96daXnz+1SdLPr/pMXALRuXDfBY9avXPF/F8zc0ZqTQVRMLJuOXaZdgxoMaKe5siIxZYrpYVa+FCuOXCV/nlx0a1Ij0fnwAtq52D+5JyuO32bnJSseOniwalh7qhgWSfZ5smRRyJMzO3lyJp+owqJiWH7sNgdvPEc3b24md2tEv+Y1yJc7x2fjVHHx3HzmyNHrVty2dkYtBFrZslLJsBidGphiXLIwxiULU6FUEfInsWAJwNbVixmbjmDj4slP9aszd1j3BM28Rs5bj63za8YN6MKYfj9/9jp5+71lwPi5vAkIZO+quVSt+Hmr4FiVinEzF6ClpcXqBTM0linGxcUxbdY8ChcuxKa1K2Ujr0xOJvY0pqtbEDd39y8+XgjBqQuXWb1lN35v/cmWNSvGZQ1p3bQhrZs2omEdc421yEnxeRtAtqxZKVEk4U1cnzeBABgbaL7Bae3oTmxcHF2a1vqiqp5tk/vx+9qjTNlyijsvnFkwtCM62rk1jtXKlpUZvZvRwMSAqTv/ovP8/QxtU4vff66X7Bx3coQQXHnqzNyDV/EPjmBwK3MmdG1Inn8teoqIjmHX+XscuPyIwJBwChfIy/BODWlaozymZUv8Pb2UEt7+71h18E/O3LJCN782m6YO4af6n89733tmx++LNqKKi2fH/PE0r/v5JyIHF3cGTZxLTKyKA2vnY1bl89W7AKs378LWwYmtKxdQpFDCqTSAk2fO4er2mi3rV1MgiZ7rUuYgE3saK1q0CG/9A3gfHPxFf0B3Hz1l8tylGJc1ZMnM5dSuUZUcOXIkf2ASAt8Fo1sgv8YruYD3wQDoFUjYDhc+lOMBlCmuuYVtcnTz5WH/zEFsPXOHNceuc/OZI92amDHy50YULqj5ORtXKcPlxUNYdOQG2y4+4qLVK5YNaUvdil9WXx0ZE8vMvVc4fd+O8iX02TKmM9XKJmyh+9LNhzFrjuLx9h3NapSnT8taNK5mlGDTi+SEhkey9/xttpy4ggB+69aK4V1bki/P/6/sP82nr9pznLIli7Fl7ljKlCj62Xmu37Ni/LxVaOfJzR+bliRoEwBw8dotth84Sp+uHWnVpKHGeFQqFeu3bKd61Sq0bNYkVT+LlEGlpKFMWn9l5iZgjs4uokylamL95m1fdHx4RISo91M30bbX4CSbNKXGwvW7RKXm3TV25zt/66EwbNFP2Lu4azzW2dNPGHQYJbacSHpbt5Swd/cT4zccE0a9ZokKfeeI5Ycvi5CIqCSPeejgKRpP2ioMBiwVU3ZeSLAHanJcfANFq+k7heHApWLtKUsRq0rY5VKtVovdF+4Jo16zRL0Ry8RDO7dUPccnb4OCxeLdp4VJj4nCoMMoMWLxduHjn7CrY1hEpBg5b50wbNFPjFm4QYRHfv4axMfHiw17/hBlGnQSHQaNF75vAxKcQwghbOxfiYr1Wolug0YlucXh6XPnRZlK1cSN23cSHSNlDMjNrNPP4BGjhVm9JiIgiT7XSbl47dbfux0dP3dRBL77uo2Dtx86JQzrdxTvNXSIdHDzFIYt+onjlzTv7ymEED2mrRG1BiZsH/ulPN4E/d3ZsOovC8SOPy017vH5SWR0rFh05IYwHrxCGA9ZIVaeuC0io5PuSR+jihO7L1uJysNWixqj1ok7LxNP1quOXhUG3S3EkKX7xbvQlHWG/CQ+Pl7ceWYvRi3bJYw6/y7KdBotfl+xW9i5eWkc7+7zRrQeOlWUbdVf7Dh2IcGbbUhYuBg2bZEwrN9RjJ+/WkRFa+757uHlI+q06Srqt+sh/AODNI4R4sObVvsuPUXrDl1kh8ZMQCb2dPTKyVlUrF5bDPz1ty/6Y1Kr1WLHgaOi3k/dhKFZY1HGvInoNniUOHX+8hddxT94aiMM63cU1ywTbkQRFxcvGvYbJ3pPXJTo8S9dPEWNvlNFjb5TxXPH16l+/kTP6+otBi7aIwy6W4iO0zYJu9e+SY73DgwRY7ecEwYDloo6YzeKJUdvChs3v8+So1qtFpefOokmk7cJgwFLRb9lR4VvUOJX+X/esxEG3S3E5E0nUvVv5eL1Rqw5dF40GDJbGHQYJar1mSzmbT8u3H39Ez3mjpWNqPrzMFG98whx92nCTbcdXT1Ek57DhVGjzmL3H+cS7X/+2tNLNOzQU1Rv1kE4OLsmGecjqyeiTKVq4sgxzRt9SBlLShO78mHsf8vc3Fw8efLkP3/e/9Kho8eYvWAJv/82nLGjRnzROYQQ2Du6cO3OPf66dgsnN3cMSpWgX7dOdGnXGp38mueo/y0mVkX1tn3o0b4lc8cPS/D4lqN/smLXMc5tXoCJkYHGc7j5vOWXuZsJDA6jZ6t6tKtfnRoVDL96CboQggsPbJm7509CwqMY0akRY7s3S3Je++ErT7acf8h9ew/i4tVkzaJQqVRhgiOieB8WRXh0LGWLFmRG72Y0MS2T6E3fV55v6GyxlcqGRTk0e0iyN0ZjVCpOXn/Ekcv3sHX1QlEU6pka07NlXVrVqaqxH86nn3HP6css3nYYo9Il2DZvHKWKfn4j+9rdR4yft5rcuXOxacFUzE0T3iQFsLK24bfJs1Gr1ezduIIqFZPevHvUuEk8eGTFvRuX5EKkTEBRlKdCiISNmf49Tib2b0MIwZQZczh19k9G/jqYiWNHf1WvGCEEV27dZdu+w1jbOqBbsAB71i/DpELKmmKNsFjCM9tX3Du1K8Gep8Gh4bT+dRo6ebU5u2k+OROpQAl4H8qcbce5bvWSWFUcRXR1qGdqTJnihSlTohAGRQtRqGA+CuTNk+qEHxweycJ9Fzl5+zm1KxmyYVxP9JNYsQrwPjyKq8+ceen+Bu+AEHS0c1FAOycVShaic73KZE9kgRFAZHQsnaZvJiQiigvLRyf5XKq4eE5cf8jGPy7hG/ieSoYl6NqsNu0aVKewbtI3yKOiY5izcT8nLt+hVX1zVk0dTp5c/2+lLIRg26FTrNh2AJPyZdm2xIIi+gm7SQohOHjiLAtWbqB40cLsWruUMgZJ7x3s6+tHkzYdGDygH9MmjUtyrJQxyMT+HVCr1cxesJgjx07Sq3tXZltM+WzRyZeysX/FqKlzCA4JZevKhdSvZZbsMdfuPmLYtMVsX2pBiwYJ9hrnjpUNv1isoHe7Ziwc+0uSb0JhkVHcsLLl4r3n2Dh78iYo+LPHs2bJgq6ONiUK6WJQVJ/SRfUxLlWUeqbG5Euk1PGT03essdh+hry5c7BhXC9qVzJMcvyXEEIwZcspTt5+zoGZg6hfJfGe4/dfODJ90xE83wRSzdiACX3b0aBahRS9Sbt6+jJqwQacPXwY3acTYwd0/uwNTxUXh8XyTZy8eIP2zRuy3GLMZ828PomIjGTu8nWcPH+ZJvXrsGbBDPLnS/pND2DpyrXs3n+QW5f+pFixosmOl75/MrF/J4QQrFy7ga0792BSuSLrVy6jdKmSyR+YjLcBgfwyZgqvPb3YvHw+zRokXHz0T6q4OBp2HUpFozLsWTlb45ilO46w/dhFxvT9mfG/dE1xLBFRMbz29cfDL4CA4FACg8PwDwrByz8Id9+AvxN/1ixZqF7BkKZmlejZqh66+TUnJ0fPt4xcdRjPt+8Y16MZI39uTNY07Dq44sgVNp++ze/dmjK+RwuNY2JVcaw+dJ7tp69jUEyfGYM708zcJEUJXQjBicuWzNu0n5w5tFg9dQSNapp+NiY8MpJRM5dh+dia3wf1YuzgXhrPbfvKid8t5uPh5cOYoQP4/deEq4c1CXr3jqatO9C0cUPWrVya7HgpY0hpYpc3T/8jl65eF9XqNBSmNeuLs+cvpsnGwO/eB4sO/X4VxrWbi+cv7ZIdv3bXEWFYv6Nw8/TR+Hh8fLyYunKHMGzRT8zbuF9ERCZdiphS0TGx4pGts1hx4JzoMH6pMOgwSlTsNl4s3HVS+L/TfGMzNCJKjFlzVBh0txC95+4UPgFfVxkkxIcbq1tO3xYG3S3EtK2nEv03cPHy+zvO6RsPi4gozZUpmtg5u4vu4+YLwxb9RM/xC4RfQMKKFf/Ad6L9oHGiXKOfxR9/Xk001h0H/hDGtZuLej91Ew+fPE9xDEIIsWjZSlHOpIZwcf2y0k3p+4Ssivn+ePv4iK59BogylaqJwSNGC08v768+Z0hoqKjbtqvo0PdXEZdEyaAQHxJK+SZdhMWyTYmOiYuLF/M2HRCGLfqJur3GiDPX76X57vQuXn5i/Op9okyn0aJC13Fi7eELIiY2YbWPWq0Wx28+FZX6zRWV+88Vm0/fEqHJ1L0nxvNtkBi56rAw6G4hRq85IuI0VMCo1Wrxx5X7okLXcaJan8ni0n1rDWfSzMHNU0xYukWUadlf1OgyQhy9eFNjlY2982vRoOtQUal5d3HjvpXGc4WGhYsRk2YJQ7PGYvikmeJ9cOpq9+3sX4nypuZi6sw5qTpO+v7JxP6dUqlUYtfeA8LErK6oVKOO2Lx9p4iJSbomOzl/Xr4uDM0ai4PHzyQ7duaKLcK4cRfh7Zd4WZ4QQli9dBQdRs4Uhi36iXbDZ4i1+08KawcXEReXdrXQbj5vxejlu4RBh1Gi9ehFwsbZQ+M4z7dBYvCSfcKgu4Uw/WW+WHHkinibyJX+v/m/DxVzdv3596KojSdvakzqoRGRYuzKvcKgwyjRZ8Y68TYoONlzx8SqxMU7j0WvCQuFYYt+osJPg8SS7UdESFi4xvGXbt0XlVv0EHV/HiRsHJw1jnnl7Cqade4nytVqKnYc+CPVb6rRMTGiTaduok7jFuLd+6//lCN9X1Ka2OUcezrx9XvDwqUruHztBoYGpZljMZWG9ZOeJ0+MEIJ+Iyfg4OzKzdOHkryx5vs2gGa9RtChRSNWzBib5Hnj49WcvGrJ0Qs3eeHohhCCfNq5KV2sMEX1C1JEryD58+YhZw4tcmppkTtnDvLlzYPOx6/SxQqTO1fCzbT/7drjl8zcfJTA4DAGd2rKuN4/kTtnwpuIL1y82Xr2Dpcf2yOEwKCILiZlimFSpjg62rnIoigoikJQaAT2r32xc/fDzTeQLIpCj2ZmjO3WLEEbA7VazelbVizbd5agkDDG9W7Hb900bwcIH0pH7z6z5dKdx1x98IzQ8EhKFNGjX4cWdG/T6LOt6z5RxcWxavshth8+RbVKxmxdPJ1Cegk7cl64epPJc5eSV/tDK+ZaNaom+9r9U2ysirGTp3Hl2g12bllP00aaWwxIGdd/cvNUUZTuwFygIlBLCJGibC0T+//dsrzL/MXL8fD0onWLZsycOumLKhjsHZ3p0G8Yv/bvxbTfhyc5dunmfWw/fIqTW5dT3STpOuhPgoJDufvMlsc2jvj6B+IX8A6/gHeERUQmeoyiKBiWKEKlsqUxNzGmXePa6Oporr0PDY9k6b6zHLl8j+KFCjJ/eA+a1TTRONbNN5Bbzx2xcvDAxs0H38DgBGOK6eankmFRqpQpTof6phgWTdgb39bViznbjvHs1WuqGRswZ1g3qhkbJBgnhOCJnRNnrt3j/K1HhEVEkk87Ny3r1uCnxrVpZG6a6BvBC3snpi/bxCtXd/r83IZZY4aQ41/lpEIINuzcz9ptezAzNWHT8nkU0tO8gXZiYmJiGDV+MjdvWzJr+mR+6dcnVcdLGcN/ldgrAmpgGzBJJvYvExMTw869B9i8fRcAM6ZMoHePbqmue580Zwnnr97g+skDFC+aeLvb8MhIWvT+DZ38+TixdSnauZMuQUyKEIKYWBVRMTFERscQGhZBcFgE70PCcPb0wcHVEzsXD3zeBpIta1baNDSnf6eW1EzkDcXK3pUZm47g7PWG5rVMGNW9DdWMSyf5WgSHRxIRHYtQC9RCkDd3Tgrk1fwzxcerufPcgUOXLLlhZUfBfNpM+6UTXZrWSlBt4uH7luOX7nDm+j18/YPIlVOLNg1q0qFpXepVr/z3BhmaBLwLZvWOgxw7f41CugWYN2E4rRrVSTAuIjKSqfOXc/HaLbq0a82iGRNTXRLr6+vHuCkWPH1uzYI5M+jTI+Em5VLm8J+WOyqKcguZ2L+ar68fFnMWYHn/AS2aNWHJ/NkULFAg5ce/8adF1/60atqQtQtnJjnW8vFzBk+eT6PaNdi+xEJj58e05ODmyfFLdzh5xZKwiEga1zTFYngfjEoXTzA2VhXH7nM32Xz8MmGR0ZiWK8WAdo1o16BGoounkqJWq7Fz8+aGlS0nrj/C2z8IPZ289GpVn187N/+s66IqLo5LllYcuXCThy8cyJJFoaFZFTo0rUvrBuafLS7SxOaVMwdOXuTP65ao49X07/oT44b0IW+ehG807l7ejJg4Exd3T6aMHsav/Xum6s08OjqanXsPsHXnbrIoWVg8fzbt2ya+PaKU8X13iV1RlGHAMIBSpUqZeXh4fPXzZkZqtZo9+w+xcu0GdHTys2fbJiqUT9nqUoAVm3awde9h/jy4nUrljZIce/D0X8xetZXeHVuzYNKI/2SH+sioaA6fv8GGQ2eJjIqmb4fmTPila4J9WAHCI6M5fesx+y/cwcXrDTm0slOjvCE1KhpSwaA4JQvrops/L7r5tVGAGFUc0TGxBIWG89rHH3ffAJw8fblv40RgcBiKolDHxIg+bRvQqrbpZ1fcPm8DOX75Dscv3cYv4B2lihaie+tGdGnVkKL6ie9QJYTA+bUX1+895tLtB7x85UKeXDnp3KYpv3TvQJlSCd+4AK7fuc/EOYvJkiUL6xfPpkHt5EuTP1GpVJw+d56NW3fg4+tHm5bNmT55AiWKJ2xFLGUuaZbYFUW5Bmj6XD9DCHH245hbyCv2NGXv4Mivo8cSEx3D/p1bqZRMT5BPQkLDaNFtAEUL63Nqz+ZkN+VYse0AWw6coFOrxiyZOkrjysdv4V1IGGv3neTwhRsUyKfNpME96N66kcY3FyEED186c+3xS57Yu2Ln5o36U1lXMorq6WBesSxNzCvTqHpF9P7ROiA6JpbL955w4vId7j+3B6B+9coM7NyKprWqJvpG5+cfyCNrW6ys7bG0WDsjcQAAGMBJREFUeo63nz8AJuXL0rVtM7q0babxCh0+TLut2rKLnQePUbm8EZuXz6dk8ZTdU4mNVXHyzDm27tyNt48vJpUrMnXCOOrVqZWi46WM77u7Yv8nmdhTxtPLm76DfiUiIpKDu7enOLlfvHaL0dPmMvG3oYwa3C/JsUIIthw8ycptBzAyKMnyGWMTbL32Ldm5uDN34wGe2jlRxdiQmSP7Jjr//klkdAyvffx58y6YoOBwgkLCAMiplZ0cWtnJr50bw+KFMCiqn6C6JiZWxb3ndlyytOLy3SeERXyoaunaqiHdWjWieOGEN1mD3ofw8NlL7j+14f7TF3j4vAEgr3YealerTLN6NWlS10xjj5d/emL9kukLV+Dq7km/7j8zY9zIFG2iolarOXX2PGs3bsHvzRuqmVZh9IhfadKowVf1H5IyHpnYMwlvH196DRiCEGpOHT1A4UIJt7fT5Pfp87hw7RZbVyygZZPkN9a+8+gZU5dsIOBdMIO6d2DckN7kyf3fdAMUQnD2xn2Wbj+K/7tgqlYow8BOrWjbqFaiHRNTc24XT18evnDgobU9lk9fEh4ZjXbuXLSqb0bXVg2pbVrhs6tzIQR2Tm7cuG/F9XtWvHzlAoB2ntzUqW5CnRpVqF3NhAplS6fo3kTQ+2BWb9nFkVN/UqxIYRbPmEijuim7yn7+wob5i5djY2tH1SomjBs9kob168qE/oP6r6piOgMbAH0gGLAWQiR790Ym9tR55ehEj36DMDYqy6G9O1NUNREVHU3vYeNwcn3Nvk0rqFnNNNljQsMjWL51P4fPXEInX14GdG3HL93bo5OChlNpISIqmpOXLdl/7ipuXn7o6uSjkXkVzCobU71SOcqUKJpoolfFxeEfFIyPfxCvvf1wdPPCycOHV26evPt4RV9UvyANzarQpmHNBFUtQghe2Dtx/sZd/rp5Hz//QBRFoVolY5rVM6e+eVVMypcjWxIdI//N581bdh08xtHT54lVqRjUuxvjhv9CnhRUIYWFhbFw2SpOnD5L4UL6TJkwlo7t2v4n90Gk75dsApbJXLpyjVHjJzOgby/mWExN0TGB797TY+gY/N76s3LudNq1bJqi417YO7H5wAmuWj5CO09u+nVuS4/2LTEo8d90CFSr1dx7Zscff93i8UtHAt+H/P2Ydu5cFMinjXbuXMSq4ohRxRIVHcv70DDU6v//LufKqYVR6RIYG5TA3MSYOlUrUrKIfoIr3Veu7py7eofz1y3x9vNHK3s2GtSsTpsmdWlS1wy9AqnbtzY8IpLb9x9x6cYdLt+4A0Cnti0YPrAP5QxTtmfrI6snTJo+i7f+Afw6aAC/DRtKnkTm7KUfi0zsmdCiZSvZvf8QG1Yv56fWLVN0TND7YEZMmsnTF7aMHzGY0UP6p/hjvIOLOxv2HuXKnUeo1WrMTSvRpU1TGtSsSomiX7a5dWoJIfD088fe1RMXDx/eh4YTHBpOeGQUWtmzkTOHFjm0sqNXID/F9HUpql+QUsUKU6qofqJXt05unvx16z5/3byH02tPsmbNQn2zqnRo2YiWDWqRL692iuOLiIzExt6R5y/teWL9kvtWT4mNVaFbQIeObVowuG93ihdJ2WsVG6ti9fpN7Ny7n9KlSrJq6UKqmVZJcSxS5icTeyakUqno/ctQnJxcOH54H+WNyqXouJjYWCwWruT0xSs0rFOTJTMnU6xIyubqAd4EBHHm8i1O/nUDVw9vAIoV1qd2tcpUNCpDsUJ6FC2kR9HCeugV0EnVdMV/xeeNP5duP+DM5VvYObmhKArmphVp37whbZvWS9GVeaxKhYOTKzb2r7B1cOKlgyPObq+Jj1cDYFCqBE3r16F104aYVTVJ1doAX18/xkycirXNS3r36IrF5Ink/o/ucUgZh0zsmdSbt/783KMvOXPm4MShfeilcOm5EIJDJ8+xdN0WsmTJyuxJo+navk2qbsIJIXjl6oHVCzsePbflsbUdQcEhn41RFIWCOvkopFuQapWNaVy7BnXNTBMt//tW4uPjsXd+zZ1Hz7h85yG2jq4AmBiXpetPzfipWQP0CyadzGNiYnj8/CX3Hj/lmY0tLx0ciYmJBaCgTn5MKhpTpWJ5zKpWoZpJxRRvVfhvN29bMmn6LOLi41m2YA5tWmnuES9JMrFnYjYv7egzaCilSpZkz7aNKa6UAfD09mXq/GU8evaCxvVqsXD6hCTbDyRFCEFIWDh+bwPx9Q/kTUAg/kHvCQh8j59/IE9s7ImIiiZr1izUNK1E93YtaNOkHrk0NPhKCzGxKp6+dOCq5UMu3LhH4LsPPWSqVy5P68Z1aNWobrL3CdRqNfceP+XUhctcu32PiMgotLJnp3IFI2qYmlC9SiWqmlSkWOFCX12ZEhMTw+oNm9m5Zz8Vyxuzcc0KDEonvd2d9GOTiT2Tu/fgISN/n0j+/PnYvXUjRuUS397t39RqNQeOnWHFpu0ATPxtKAN6dE7ztgKxKhXPbR2xfPycCzfv4eHtR17tPHRs0Yh2zepTs2qlr3rOqOgY7JzcsLZ34t6TFzy2tiUqOoYcWlo0q2dOq0Z1qGdeNdkrc4DQsDBO/HmJgyfO4u7pTf58eWnTrBGtmjSkjnk1cuVMvktlatjaOzBp+iycXVzp07MbM6ZMJGcaP4eU+cjE/gOwc3jFkBFjiImNYeGcmfzUumWqriJ93rxl1pI13Lr3kKqVK7Ji7rQUV26klhCCx9Z2/HH+Kpdu3Sc6JhZdnfyYValAlQrlMCxVHMOSxSleWI8cWlpoaWVHURRiYmIJDgsjODQcbz9/XD28cHb3wsH5NY5uHn/Pb5cpVZyGtarRoGZ16lQ3SXENfkxMDFv2HmbHgT+Iio6mhmll+nX/mbbNG6fJ/rT/FhkZxfbde9myYze6BQuwZP4cGjesn+bPI2VOMrH/ILx9fBk1fhK2dg60aNaE+bOmp2pqRgjBn5dvMG/FOiKiopg4cgiD+3T/pk3BIiKjuP3wGVfvPsLa3gkPbz+N47JlzUpcfHyC/19ItwDGZUpTrZIxVSsaYVrRCH3dlDdL+8TyoRWzl63Fw8uHdi2bMmJgHypX+DarbmNjVRw9fpJN23YSGBREx3ZtmTtjGvm/cF5e+jHJxP4DiYuLY8+Bw6zZsBktrexM/H00vbp3IXv2lK/aDAh6x6wlq7ly6y5mVU1YNc+CUiX+m6ZSEZFRePj48drTlzeBQcTEqoiNVRGrUqGdJzc6ebXRyZeXwvoFMTIomapyRE1Cw8KYsXg1F67exLBUSeZPG0f9WmZp9NN8Liw8nNNnz7Nr3wG8fXypZV6DSePGYFa92jd5Pilzk4n9B+Tu4cnMeYt48OgxZQwNmDphLM2bNk7x9IwQgrN/XWXO8nWo1WpmTRxD945tM9XydSfX1wyfNBMf3zeM+XUgwwb0SvMpFyEETs4uHDl+klNn/iQiMpKqVUwYO2oEjRrUy1Svp/Tfkon9ByWE4PrN2yxbvQ631+7UrmnGrGmTqVghZQ3E4MPc++Q5S3j41JpWTRqweOYkCuqkbgXm9+jyTUsmzVlMrlw52bRsXoraLKSGo7MLZ/+8wOVrN3D38EQre3Z+atuKAb17UdVU825QkpQaMrH/4FQqFX+cOM26TVsIDgmlf5+ejB89krx5U9b3Ra1Ws/vwCVZu2kH+fHmZP208rZtmzD001Wo163fsY/2OfVStXJEtK+ZTpJB+mpw7NDSM839d4vips9jY2pEtWzbq1DKnVfOmtG7ZAj3dxHu5S1JqycQuARASEsrq9Zs49MdxdAsWZP6s6bRu2TzFxzs4uTBp7hIcnFz5qUUT5k4Zi17B1N+oTC/hEZFMmrOYK7fu0rV9axZOn5CiVrnJee3uwbZdezh34RIxMTGUNzaie+dOdOrwU6p2vZKk1JCJXfrMSzt7Zs5biK2dA316dmPm1EkpTnCquDi27zvChp370c6Tm0mjfqVbhzbJbuKR3qysbZi1eDWuHp5MHzuSQb1Tv4/sv8XGqti2czebtu0kS9asdP25Az26dsakUkU5dy59czKxSwmoVCpWrdvEjj37qFShPBtWL0/VSkcn19fMWLyKpy9sMSpjwLTfR9Ckfu3vLqG9cnFj5aYd3LB8QCE9XVbOm56qrecS4+v3hhFjxmPn8Ir2bVsza9rkFLd0kKS0IBO7lKgbt+4w2WI2aqFm15YN1KhWNcXHCiG4fNOSZRu24eHlg3m1Kgzu052Wjet/8w2xE6NWq3FwcsXyoRWWD614+NQa7Ty5GfFLH37p1TVNVo36+PrSo/9gwsMjWLF4Pq2ap6wFsiSlJZnYpSR5efswYOhIAgMD2bpxDfXr1E7V8bEqFUdP/cmuw8fx8vGjeNHC9O3aidbNGmFYqkSaxalWq3kXHEJA0DsCg94T9P49Qe+CCQgMwsvXDy9fPzy8fAgLjwCgglFZWjZpwKBeXb+4Kde/BQYG0XPAYN69f8/hPTtSVWEkSWlJJnYpWf4BAQz89Tfc3T3YuGYFzZs2TvU54uPjuW55n71HTvLwqTUAhqVK0rCOObXNqmFc1oBSJYqTPZH5eCEEgUHv8PJ98yFRe/vi4eOLl48fXj6+BAS+07j6VCt7dooXLUKpEkUpUawo1U0q0aCOOYXSeGokLDycvr/8iutrd/bt2IJ5DbmwSEo/MrFLKRIcHMIvw37DwdGJzWtXflFy/8TLx4+bdx9w3fIBz2xsiYiMAiB7tmwU0tclZ44c5MyRg2zZshEWHk5IaBghoWEJEnchPV1KlShGqeLFKFxIj0K6uujrFURPtyB6BXTQLViAfHm1v/ncvlqtZsSY8dyyvMe2jWto2ihjlntKmYdM7FKKhYWFMWDoSF45OrFlw2qaNEx+8+vkREfH4PzaHRc3D5zcXhMQ+I7omBiiY2JQqeLIl1ebfHm1yZ8vL0X09ShRvCglixWlRLEiad5J8UsIIVi5dgNbd+5hjsVUBvTtld4hSZJM7FLqhISE0n/oCJxdXNm2YQ2NGtRL75DSjRCCpavWsnPPfnr36MqC2TO+u8of6ceU0sQutzyXAMifPx/7d2yhXBlDho8Zj+W9B+kdUrqIjVUxY+5Cdu7ZT/8+PZk/y0ImdSnD+arErijKCkVRXimKYqMoymlFUTJ+Q5EfmI5Ofvbv2kpZQwOGjxnPI6sf61OVq9truvUdyB8nTjFy2BDmWExNdENsSfqefe1v7VXARAhhCjgB078+JCk9FdDRYd/OLZQqUZxffxvL8xc26R3SN6dWqzn8x3E6du+Dr68fW9avZtLY0fJKXcqwviqxCyGuCCHiPn77EEi7AmYp3egWLMj+XVvR09Nl0PBR2Ly0S++QvpkHj6zo3Ksfs+YvpmaN6lw4/YdcfCRleGn5OXMw8FdiDyqKMkxRlCeKojwJCAhIw6eVvoVC+voc3L2dAjo69B86ggePrNI7pDRl7+DI0N9+p9/gYbx7956VSxawO5Ubg0vS9yrZqhhFUa4BmraxnyGEOPtxzAzAHOgiUlBmI6tiMg6/N28ZNHwU7u4eLJw7i26dO6Z3SF/lydPnbNm5m1t37pI3rza/DRvKwL690qTjoyR9aymtikm2PZ8QokUyTzQQaA80T0lSlzKWokUK88f+3YyZOIWpM+fg5OzMlAljv/vOjv+kUqm4euMWew8c5ulzawoW0GH8mN8Y0KcX+fKlrD+9JGUkX1XHrihKG2A10FgIkeL5FXnFnvHExcWxaPkq9h86SqUK5ZkxdRJ1an19x8RvKSw8nGMnTrP7wCHevHlLqZIlGNivNz27diZXrlzpHZ4kpdp/skBJURQXIAcQ9PF/PRRCjEjuOJnYM65LV66xaPkqfP3e0LJ5Uyb8PgrjcmXTO6zPeHh6sf/QUU6cPkt4RAS1a5ozZGA/mjRqkG4dKCUpLciVp9I3Ex0dzZ4Dh9iyfTcRkZHUqFaVTu1/onWLZujr66VLTEIIHj5+wu59B7l5x5JsWbPSrm1rBvbrjalJ5XSJSZLSmkzs0jcX9O4dp8+d58Spszi7ugFgVK4stc3NqF3LnOpVTSlSuNA3rQePiY3lyrUb7Ny7H1s7B3R1C9KrWxf69uouK1ykTEcmduk/5eTiyo2bt3lo9ZSnz54TGfWhs6O+nh6mJpUwrWJC5YoVqFihPIUL6X91sn/t4cHR46c4deYc794HY2hQmiED+9OlU3tZ4SJlWjKxS+lGpVJh7+CI9cuX2Nja8dLWHrfX7nz6XSugo0OF8sZUMDaivHE5yhgaULpkSXR1Cyaa8CMiIrF++RLLuw+wvHefV07OZMuWjeZNGtGre1ca1Ksjl/9LmZ5M7NJ3JTwigleOzji8csT+lSOOTs44ubgQFRX995g8uXNTpEhhcuXKSa6cOcmePTtB797z5s1bQkJDgQ+93c1qVKdRg3p07tiOQvr66fUjSdJ/TiZ26bsXHx+Pp7c37h6eeHp54+npzVt/f6Kio4mKiiY2NgbdggUpWqQIRQoXwtioHLVrmpMnT+70Dl2S0kWaLVCSpG8la9asGJYujWHp0ukdiiRlKnJSUpIkKZORiV2SJCmTkYldkiQpk5GJXZIkKZORiV2SJCmTkYldkiQpk5GJXZIkKZORiV2SJCmTkYldkiQpk5GJXZIkKZORiV2SJCmTkYldkiQpk5GJXZIkKZORiV2SJCmTkYldkiQpk/mqxK4oygJFUWwURbFWFOWKoijF0iowSZIk6ct87RX7CiGEqRCiGnAemJ0GMUmSJElf4asSuxAi9B/f5gH++332JEmSpM989dZ4iqIsAgYAIUDTr45IkiRJ+irJXrErinJNURRbDV+dAIQQM4QQJYFDwOgkzjNMUZQniqI8CQgISLufQJIkSfqMIkTazJ4oilIauCCEMElurLm5uXjy5EmaPK8kSdKPQlGUp0II8+TGfW1VjNE/vu0IvPqa80mSJElf72vn2JcqilIeUAMewIivD0mSJEn6Gl+V2IUQXdMqEEmSJCltyJWnkiRJmYxM7JIkSZmMTOySJEmZjEzskiRJmYxM7JIkSZmMTOySJEmZjEzskiRJmYxM7JIkSZmMTOySJEmZjEzskiRJmYxM7JIkSZmMTOySJEmZTJr1Y0/VkypKAB+6QaY3PSAwvYNIgYwSJ2ScWGWcaSujxAkZJ1ZNcZYWQugnd2C6JPbvhaIoT1LStD69ZZQ4IePEKuNMWxklTsg4sX5NnHIqRpIkKZORiV2SJCmT+dET+/b0DiCFMkqckHFilXGmrYwSJ2ScWL84zh96jl2SJCkz+tGv2CVJkjKdHz6xK4qyQFEUG0VRrBVFuaIoSrH0jkkTRVFWKIry6mOspxVF0UnvmDRRFKW7oih2iqKoFUX57ioPFEVpoyiKo6IoLoqiTEvveBKjKMpuRVH8FUWxTe9YkqIoSklFUW4qiuLw8d99bHrHpImiKDkVRXmsKMqLj3HOS++YkqIoSlZFUZ4rinL+S47/4RM7sEIIYSqEqAacB2and0CJuAqYCCFMASdgejrHkxhboAtwJ70D+TdFUbICm4C2QCWgt6IoldI3qkTtBdqkdxApEAdMFEJUBOoAo77T1zQGaCaEqApUA9ooilInnWNKyljA4UsP/uETuxAi9B/f5gG+y5sOQogrQoi4j98+BEqkZzyJEUI4CCEc0zuORNQCXIQQbkKIWOAo0CmdY9JICHEHeJfecSRHCOEnhHj28b/D+JCMiqdvVAmJD8I/fpv949d3+beuKEoJoB2w80vP8cMndgBFURYpiuIF9OX7vWL/p8HAX+kdRAZUHPD6x/fefIdJKKNSFMUAqA48St9INPs4vWEN+ANXhRDfZZzAWmAKoP7SE/wQiV1RlGuKothq+OoEIISYIYQoCRwCRn+vcX4cM4MPH38Pfc9xfqcUDf/vu7xqy2gURdEGTgLj/vUp+LshhIj/OOVaAqilKIpJesf0b4qitAf8hRBPv+Y82dIonu+aEKJFCoceBi4Ac75hOIlKLk5FUQYC7YHmIh3rVFPxen5vvIGS//i+BOCbTrFkGoqiZOdDUj8khDiV3vEkRwgRrCjKLT7cw/jebk7XBzoqivITkBPIpyjKQSFEv9Sc5Ie4Yk+KoihG//i2I/AqvWJJiqIobYCpQEchRGR6x5NBWQFGiqIYKoqiBfQCzqVzTBmaoigKsAtwEEKsTu94EqMoiv6nSjJFUXIBLfgO/9aFENOFECWEEAZ8+P28kdqkDjKxAyz9OI1gA7Tiw93o79FGIC9w9WNp5tb0DkgTRVE6K4riDdQFLiiKcjm9Y/rk483n0cBlPtzkOyaEsEvfqDRTFOUI8AAoryiKt6IoQ9I7pkTUB/oDzT7+Xlp/vNr83hQFbn78O7fiwxz7F5USZgRy5akkSVImI6/YJUmSMhmZ2CVJkjIZmdglSZIyGZnYJUmSMhmZ2CVJkjIZmdglSZIyGZnYJUmSMhmZ2CVJkjKZ/wGbTjGhYf95jgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(approx.sample(1000)['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we had a `trace_cov` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.00494398 0.46960795]\n",
      " [0.46960795 0.97373728]]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    print(pm.trace_cov(trace))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can estimate the same covariance using `Empirical`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elemwise{true_div,no_inplace}.0\n"
     ]
    }
   ],
   "source": [
    "print(approx.cov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's a tensor itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.0044415  0.46937314]\n",
      " [0.46937314 0.97325041]]\n"
     ]
    }
   ],
   "source": [
    "print(approx.cov.eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimations are very close and differ due to precision error. We can get the mean in the same way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.00523404 -0.00168637]\n"
     ]
    }
   ],
   "source": [
    "print(approx.mean.eval())"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
